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Math education

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shvarz:
Found (through LJ) an interesting essay on math education in school: http://www.maa.org/devlin/LockhartsLament.pdf

25 pages, but worth reading when you have time. I certainly found something there to think about.

Numsgil:
I'll try to read it tonight.  Coming from an actual math background, I'd say the present mathematical educational system is problematic (at least in my experience) because it hasn't figured out whether the calculator is a good thing or a bad thing.

For instance, I learned how to do long division.  I can still do it.  But I almost never do, because the calculator is faster and less error prone than my pen and paper.  Sometimes when I'm at the grocery store, I have to do some division to figure out cost per item and things like that (though usually it's pre-calculated on the price sticker nowadays), but is that rare use worth the months and months of elementary school we spent learning to long divide?  Especially when it's so distasteful?

On the other hand, learning to do square roots by hand was always something I wanted to do.  It bugged me that I had no idea.  Most people I asked said to use a calculator (or the really old geezers-- a slide rule).  It wasn't in to calculus with Taylor series that I had any idea how to do square roots with anything but guess and check.  Here I had an honest desire that was left unfulfilled for years.

More recently, I got a B in my ODE class.  In theory, I should be able to solve y''(x) = -b * y'(x) for an equation in the form y(x) = ...  But whenever I come across such an instance, I always load up Maple and do it in there.  I don't hardly remember how to do those ODEs by hand anymore, and Maple is way less error prone.

In 100 years when the school system has figured out that having calculators means people don't need to do math by hand well, I think things will improve.  Teach me how humans and computers solve a problem, then give me the computer and let me go on with my life   I don't do square roots by hand now, even though I know how.  I still use the calculator.  What I want to learn is what to actually do with the tools I learned.

Shasta:
I very much agree with what Numsgil said. I have alg2/trig and AP Chem right now in high school, basically two math classes. On one hand in alg2 for most of our tests we can only use a old four function calculator, and only get to use a graphing when dealing with things like logs. On the other hand in AP Chem we have a class-room set of TI's new Inspire CAS series and can use them how ever we like. (The Inspire CAS can do things such as solve algebric equations, do logs of x root and so forth)

What I would like to see is a lot more self teaching, instead of telling me what each part of y=ax2+bx+c does, have them graph the equation and drag different parts around and see how the equation changes. Learning like this would make the information more meaningful to the students as it is gained first hand instead of just having it told to you.

EricL:
I'll push back a little.  One the one hand I agree that it's difficult to learn anything you arn't really interested in and that the best teaching occurs when the student has natural curiosity about the subject matter, whatever it is.  Many of us are here soley becuase we have that natural curiosity w.r.t. ALife and DB.

But I do think there are certain basics, in every subject, that every last person should always be taught even though technology makes that method unlikly to be used often in real life.  Should we stop teaching history becuase you can look up anything you want anytime on the web?  You won't always have a calculator in your pocket (or an internet connection - or maybe you will) but more importantly, for math in particular, I'll argue that some understanding of the underlying process being performed by the machine is important to hold onto at least at some level even if you use the machine all the time.  It provides some intuition as to the correctness of what the machine produces for one thing not to mention an understanding of related topics such as the precision of the answer and the execution cost of the underlying algorithim.  Perhaps not critical for everyone, but I want the engineer building the bridges I drive on to know the difference between using a 16-bit calculator and a 32-bit calculator and what that means for his/her results.  Every sci-fi series ever done has some story about meeting the civilization whose inhabitents no longer know how the machines keeping them alive work...

"Anyone who cannot cope with mathematics is not fully human.  At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house."  Robert Heinlein, Time Enough for Love

abyaly:
Did you read the article? The problem is that math isn't really being taught in schools. People are being trained to preform tasks that were discovered through math, but the math that led to the discovery is left out. Then they are told that's what mathematics is. It's criminal. Even at the university level, many 'applied math' courses strip out the mathematics and only deliver formulas and equations.

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